Plane trigonometry, by S.L. Loney.

14

TRIGONOMETRY.

[Exs. III.]

17. The difference between the two acute angles of a right-angled
2
triangle is -rt radians; express the angles in degrees.
2 3
18. One angle of a triangle is 2x grades and another is 3x degrees,
whilst the third is 7 radians; express them all in degrees.
75
19. The circular measure of two angles of a triangle are respectively
1 1
2 and;what is the number of degrees in the third angle?
2 3'
20. The angles of a triangle are in A. P. and the number of degrees
in the least is to the number of radians in the greatest as 60 to 7r; find
the angles in degrees.
21. The angles of a triangle are in A. P. and the number of radians
in the least angle is to the number of degrees in the mean angle as 1: 120.
Find the angles in radians.
22. Find the magnitude, in radians and degrees, of the interior
angle of (1) a regular pentagon, (2) a regular heptagon, (3) a regular
octagon, (4) a regular duodecagon, and (5) a regular polygon of 17 sides.
23. The angle in one regular polygon is to that in another as 3: 2;
also the number of sides in the first is twice that in the second; how
many sides have the polygons?
24. The number of sides in two regular polygons are as 5: 4, and
the difference between their angles is 9~; find the number of sides in
the polygons.
25. Find two regular polygons such that the number of their sides
may be as 3 to 4 and the number of degrees in an angle of the first to the
number of grades in an angle of the second as 4 to 5.
26. The angles of a quadrilateral are in A. P. and the greatest s
double the least; express the least angle in radians.
27. Find in radians, degrees, and grades the angle between the
hour-hand and the minute-hand of a clock at (1) half-past three,
(2) twenty minutes to six, (3) a quarter past eleven.
21. Theorem. The number of radians in any angle
whatever is equal to a fraction, whose numerator is the arc
which the angle subtends at the centre of any circle,. and
whose denominator is the radius of that circle.